[Reily]

Anatolia never made much sense to me. Steppes of Eurasia is a whole lot more likely.

[Verginius Rufus]

This is the first time I ever heard of Anatolia as the place where horses were first domesticated. The steppe land north of the Black Sea and Caspian Sea makes more sense, as you note. The Proto-Indo-European speakers almost certainly lived in that region and they seem to be the first people to domesticate the horse--which may be a major reason why they expanded all the way from western Europe to India.

Anatolia has been proposed as the original home of the Proto-Indo-European speakers but that doesn't make much sense and is a minority opinion.

[Verginius Rufus]

Troy dates back to about 3000 B.C., but apparently the first evidence of any horses there dates to about 1900 B.C. (Troy VI). The Trojans of that period seem to be a new people unrelated to the Trojans of Troy I to V. That doesn't make sense if horses were first domesticated in Anatolia. The Trojans became famous for their skill with horses--the last word of the Iliad in Greek means "tamer of horses" (referring to Hector of Troy). So the story of the Trojan horse seems to be a joke at their expense.